Remove any loose, small bones from the inside of the quail.
Sew the bottom of the birds closed with fine, white string or close with toothpicks.
Cross the legs and tie them together.
Set aside.
Place 2 tablespoons of the stock in a large skillet and set over medium heat.
Stir in the shallots, carrots, and celery.
Cook for about 4 minutes, stirring frequently.
Add the mushrooms, tarragon, and rosemary and cook until the mushrooms have released their liquid and the liquid has evaporated.
Add the rice and pecans to the skillet and stir until combined. (Let the stuffing cool, then chill before filling the quail if they are not to be baked immediately.) Stuff the quail through the neck opening.
Fold the neck skin underneath and hold in place with a small skewer or toothpick or sew closed.
Any remaining stuffing can be baked separately in a small casserole.
Preheat the oven to 450°.
Rub the quail with mustard, then place them in a shallow baking dish and place in the oven.
Bake for 5 minutes then reduce the heat to 350°.
Baste with rest of the chicken stock and bake about 15 to 20 minutes more or until the birds are golden brown.
Remove the string, toothpicks, or skewers.